Analysis of multi-component mixtures using various analytical techniques often results in data that can be represented as a signal that is a function of two or more dimensions (or variables). An example is gas chromatography coupled with ion mobility spectrometry (GC-IMS) where one dimension is ion drift-time (td) in the IMS and the other dimension is real-time elution (tr) from the GC. Thus, the signal can be mathematically represented as C(td, tr). Such complexity has recently become relevant for IMS techniques that have responses in both the drift-time and the real-time dimensions.
A brief survey of the literature reveals a myriad of statistical two-dimensional techniques that have application for such data sets. Among these techniques are factor analysis techniques such as principle component analysis (PCA), evolving factor analysis (EFA), classical least-squares methods (CLS), inverse least-squares methods (ILS), and a number of techniques derived from these approaches (see A. de Juan and R. Tauler, Journal of Chromatography A 1158, 184 (2007); E. V. Thomas and D. M. Haaland, Analytical Chemistry 62(10), 1091 (1990); K. P. Pleibner et al., Electrophoresis 20, 755 (1999); D. M. Haaland and D. K. Melgaard, Applied Spectroscopy 54(9), 1303 (2000); and N. D. Sidiropoulos et al., IEEE Transactions on Signal Processing 48(8), 2377 (2000)). These approaches are generally designed to identify and quantify the concentration of a multi-component mixture measured using an analytical tool.
However, a need remains for a method to optimize the performance of an analytical system to provide a measurement with high quality and high fidelity. Accordingly, the present invention is directed to a method to quantify for comparison the quality and fidelity of signal response peaks. The method will be referred to herein as two-dimensional Péclet analysis.